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  1. Proceedings of the 2003 conference on APL (APL '03)
  2. Finite group tables in APL
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Simulating ordered GRB color triples using J to create images with gradients in both hue and value
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NAVPLANR (NP): flight navigation planning software
An SPMD/SIMD parallel tokenizer for APL
Bitslice: representation without taxation
Useful formulas for multidimensional arrays
An algorithm to compute all full-span sub arrays of a regular array
A new "dual-view" diagram of array structure
A generating function that counts the combinatorial full-span sub array structure of a regular array with some applications to APL
Interesting inner-product scans
Finite group tables in APL
INSTRUCTOR: a new technique of guiding the user in simulation software
Simulated APL session manager
Bit arrays from row and column sums

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Finite group tables in APL

Content Provider ACM Digital Library
Author Lipovaca, Samir Burchfield, Joseph
Abstract It is known from group theory that multiplication tables for finite groups are Latin squares. These basic Latin squares have proved useful for solving various problems, for example, problems of memory management in parallel computing systems, organizing party games, communications networking, computer imaging, and experimental design. We show how the problem of multiplication tables for a finite group G of order N can be solved using APL. The solution is based on Lagrange's and Cayley's theorems for finite groups: the order of a subgroup of a finite group G is a divisor of the order of the group and every group G of order N is isomorphic with a subgroup of the group of permutations of N objects (symmetric group SN). We demonstrate that using APL interactively offers a powerful, consistent, and simple notation for dealing with the elements of the symmetric group SN. Group tables for the groups of order 4, 6, and 8 are used to illustrate the method. Possible simplifications of the method are outlined.
Starting Page 75
Ending Page 81
Page Count 7
File Format PDF
ISBN 1581136684
DOI 10.1145/882067.882078
Language English
Publisher Association for Computing Machinery (ACM)
Publisher Date 2003-06-11
Publisher Place New York
Access Restriction Subscribed
Subject Keyword Group Permutation Group theory Subgroup Apl Multiplication tables
Content Type Text
Resource Type Article
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